\(QS87_{1}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(87\) | \(4\) | \(111010\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = P_x(x,y) \\ \dot{y} = P_y(x,y) \end{cases}\]
has the following phase portrait done with P4.
The phase portrait appears in the following papers
- With name \(CD04\) in {J. C. Artés}, Systems of class CD, {Preprint} (2026).
- With name \(A1.4L1\) in {J. C. Artés, L. Cairó and J. Llibre}, Phase portraits of the family IV of the quadratic polynomial differential systems, Qual. Theory Dyn. Syst. { bf 24} (2025), no.~2, Paper No. 66, 34 pp.; MR4860323
- With names \(22\) and \(45\) in {A. Ferragut and C. Valls}, Phase portraits of Abel quadratic differential systems of the second kind, Dyn. Syst. { bf 33} (2018), no.~4, 581--601; MR3869849Note (for name \(45\)): I assume there is a normal saddle at origin
- With names \(g2\) and \(g14\) in {J. C. Artés, J. Llibre and N. Vulpe} Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views{Applied Math. { bf 4} (2024) {70-78}}
- With name \(P03\) in {J. Llibre and C. Valls}, Global phase portraits for the Abel quadratic polynomial differential equations of second kind with $Z_2$-symmetries, Canad. Math. Bull. { bf 61} (2018), no.~1, 149--165; MR3746481
- With name \(67\) in {J. Llibre and X. Zhang}, Topological phase portraits of planar semi-linear quadratic vector fields, Houston J. Math. { bf 27} (2001), no.~2, 247--296; MR1874098
- With name \(Fig2a (II)\) in {J. W. Reyn}, Phase portraits of quadratic systems with finite multiplicity one, Nonlinear Anal. { bf 28} (1997), no.~4, 755--778; MR1420390
- With name \(jp01 Fig 2.66\) in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
- With name \(1.4L1\) in {J. C. Artés, R. D. S. Oliveira and A. C. Rezende}, Topological classification of quadratic polynomial differential systems with a finite semi-elemental triple saddle, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 26} (2016), no.~11, 1650188, 26 pp.; MR3566296
- With name \(E29\) in {B. Coll, A. Gasull and J. Llibre}, Quadratic systems with a unique finite rest point, emph{Publ. Mat.}, textbf{32} (1988), 199--259.
- With name \(Fig 37 \) in {J. W. Reyn and X. H. Huang}, Separatrix configurations of quadratic systems with finite multiplicity three and a $M^0_{1,1$ type of critical point at infinity}, Report U. Delft (1997?).